Respuesta :
Answer:
0.000064 = 0.0064% probability that the box will contain less than the advertised weight of 466 g.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
N(489,6)
This means that [tex]\mu = 489, \sigma = 6[/tex]
What is the probability that the box will contain less than the advertised weight of 466 g?
This is the p-value of Z when X = 466. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{466 - 489}{6}[/tex]
[tex]Z = -3.83[/tex]
[tex]Z = -3.83[/tex] has a p-value of 0.000064
0.000064 = 0.0064% probability that the box will contain less than the advertised weight of 466 g.
